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I've always seen spacetime shown with a ball on top of some cloth that curves around it, and I don't really understand it, since it really only has 2 dimensions and there's some sort of external gravity causing gravity? I was wondering what it would look like if that ball had more balls inside of it (like Earth contains humans, gases, etc.). Is there a way to visualize that? Does the fabric of spacetime go through everything or does it wrap around individual elementary particles? Is it even actually a fabric?

Apologies if this question is too broad.

Qmechanic
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    It’s not a fabric, and it’s four-dimensional. You’re in it. – G. Smith Dec 02 '19 at 00:32
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    Related: https://physics.stackexchange.com/q/90592/123208 That "fabric" analogy can be very misleading. Just about the only useful thing in it is that it can show how the shortest path between 2 points on a curved surface can be a curve. – PM 2Ring Dec 02 '19 at 00:42
  • Also related: https://physics.stackexchange.com/q/3009/123208 – PM 2Ring Dec 02 '19 at 09:22

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The ball sitting on top of a membrane image is wrong in many respects. A better image would be to show just a membrane (i.e. a curved two-dimensional surface) and colour different parts of the surface differently to show what is there, such as matter or vacuum, for example. Such an image can serve to illustrate the spatial situation for a static spacetime. One is showing a slice through a three-dimensional space. Such a slice takes the form of a surface, and it is a warped surface owing to the curvature associated with gravitation. You have to regard the membrane itself as the representation of space. The answer to your question is yes, it does extend through whatever matter may be around. Or, to put it another way, matter is wholly within the space we are talking about.

Andrew Steane
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